Quantum Monte Carlo Study of a Resonant Bose-Fermi Mixture

We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion component. We focus on the case where the boson density $n_B$ is smaller than the fermion density $n_F$, for which a first-order quantum phase transition is found from a state with condensed bosons immersed in a Fermi sea, to a Fermi-Fermi mixture of composite fermions and unpaired fermions. We obtain the equation of state and the phase diagram, and we find that the region of phase separation shrinks to zero for vanishing $n_B$.

Figure 1

Energy of a BF mixture at $x=0.175$ and $\zeta =1$, with the contribution of the bare binding energy of the molecules subtracted for $a_{\mathrm{BF}}>0$. Circles: JS FN-DMC results. The solid line corresponds to Eq. (3), and the dashed line is a guide to the eyes. Squares: JMS FN-DMC results. The dotted line corresponds to Eq. (5) with $M^{*}$ and $\alpha$ from 37 and $C=0$. Inset: Energy without subtracting the bare binding energy.

Figure 2

Energy as a function of $x$, for $\zeta =1$. Main figure, from top to bottom: Energy of the FF mixture at $g=0.6$, $g=0.75$, $g=1$, and $g=5$, with the bare binding energy of the molecules subtracted. Dashed lines: Equation (5) with $C=0$, $M^{*}=2m$, and $\alpha =1.18$. Solid lines: Best fit using Eq. (5) with $M^{*}$ and $\alpha$ from 37. Inset, from top to bottom: Energy of the polaronic phase at $g=0$, $g=0.5$, and $g=0.75$. Solid lines: Best fit using Eq. (4).

Figure 3

Phase diagram in the $x\mathrm{\text{−}}g$ plane, at $\zeta =1$. The dotted curve indicates the energy crossing between the polaronic (SF) and FF molecular (N) phases. It lies in the middle of a phase separation (PS) region. The gray area above $x\simeq 0.2$ indicates the nonuniversal region (for $\zeta =1$). Inset: Bosonic condensate fraction $n_0$ for $x=0.175$ in the polaronic phase. Circles: Extrapolated results from FN-DMC and VMC simulations. Dashed line: Weakly interacting Bose gas result $n_0^B=1-(8/3)\sqrt{x{\zeta }^3/6{\pi }^3}$. For $g>0.75$ the unbiased estimate of $n_0$ is no longer reliable, resulting in large error bars.